Expression of type ExprTuple

from the theory of proveit.linear_algebra.scalar_multiplication

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, Lambda, alpha, x, y
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(alpha, Forall(instance_param_or_params = [x, y], instance_expr = Equals(ScalarMult(alpha, x), ScalarMult(alpha, y)), condition = Equals(x, y))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\alpha \mapsto \left[\forall_{x, y~|~x = y}~\left(\left(\alpha \cdot x\right) = \left(\alpha \cdot y\right)\right)\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 19 body: 3
2	ExprTuple	19
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 12 body: 7
7	Conditional	value: 8 condition: 9
8	Operation	operator: 11 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	18, 20
13	Operation	operator: 16 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	19, 18
16	Literal
17	ExprTuple	19, 20
18	Variable
19	Variable
20	Variable